LogiQuest

294. Paths in a DAG

MediumTopological SortDP

Count the paths from node 1 to node n in the directed acyclic graph. Print modulo 10⁹ + 7.

Input format

Line 1: n m Next m lines: u v (edge u → v)

Output format

The number of paths mod 10⁹ + 7.

Example 1

Input

4 5
1 2
1 3
2 4
3 4
2 3

Output

3

Example 2

Input

3 1
1 2

Output

0

Constraints

2 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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